3/28/2008

Marianty Ionel
University of Toledo

Austere submanifolds of dimension 4

An austere submanifold has the property that its second fundamental form in any normal direction has its eigenvalues symmetrically arranged around zero. The class of austere submanifolds was first introduced by Harvey and Lawson in 1982. The main motivation was their result showing that the conormal bundle of an austere submanifold in $R^n$ is a special Lagrangian submanifold of $R^{2n}$. The austere submanifolds of dimension 3 in Euclidean space were classified by R. Bryant. In this talk I will present some results towards a classification of austere submanifolds of dimension 4 in Euclidean space. Depending on the type of the second fundamental form, we get both non-existence results as well as new examples of austere submanifolds. This is joint work with Thomas Ivey.